The next step is to have access to the enumeration sequence \((c_n)\)  of a class \(\mathcal {C}\)  from an equation satisfied by the generating function \(C(z)\)  of \(\mathcal {C}\) .
A possible way, especially in the case of tree-like objects, is to appeal to the Lagrange inversion formula ([1]}).
To state it, we introduce the notation \([z^n] C(z)\)  to denote the \(n\) -th coefficient of the series \(C(z)\) ;
that is to say, writing \(C(z) = \sum _{n\ge 0} \frac{c_n}{n!} z^n\) , we have \([z^n] C(z) =\frac{c_n}{n!}\) , or equivalently \(c_n = n! \cdot [z^n] C(z)\) .
